We present the first calculation of coupled-channel meson-meson scattering in the isospin $=1$, $G$-parity negative sector, with channels $\pi \eta$, $K\overline{K}$ and $\pi {\eta }^{\prime }$, in a first-principles approach to QCD. From the discrete spectrum of eigenstates in three volumes extracted from lattice QCD correlation functions we determine the energy dependence of the $S$-matrix, and find that the $S$-wave features a prominent cusplike structure in $\pi \eta \to \pi \eta$ close to the $K\overline{K}$ threshold coupled with a rapid turn-on of amplitudes leading to the $K\overline{K}$ final state. This behavior is traced to an $a_0(980)$-like resonance, strongly coupled to both $\pi \eta$ and $K\overline{K}$, which is identified with a pole in the complex energy plane, appearing on only a single unphysical Riemann sheet. Consideration of $D$-wave scattering suggests a narrow tensor resonance at higher energy.

• Received 22 February 2016

DOI:https://doi.org/10.1103/PhysRevD.93.094506